I believe it is. I don't have the particle physics background so no lab experiments to back me up on this. Most of the nuclear reactions tend towards lower mass products when compared to the reactants (e.g. hydrogen fusion, uranium fission) The only natural example of the reverse I can think of are the quantum fluctuations where out of nowhere in "empty space" an electron-positron pair can appear and then annihilate.

I know that it's possible to convert mass to energy. But is it possible to convert energy to mass?

The question is loaded with problems of semantics. E.g. you may be thinking of a proton annihilating an antiproton leaving only photons in the end products. But the only think that has changed here is the form of the energy. The total energy has remained constaint throughout the process. That is what is meant by mass-energy conversion.

Now I believe you're question is "Can we take a photon, which has zero "proper mass" and create something which has non-zero proper mass. The answer is yes. The process is called pair poduction.